Preprints 2022

Oneloop amplitudes in EinsteinYangMills from forward limits
Authors: Franziska Porkert, Oliver Schlotterer
Preprint number: UUITP04/22
We present a method to compute the integrands of oneloop EinsteinYangMills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the doublecopy structure of EinsteinYangMills as (super)YangMills with the socalled YM+phi^3 theory  pure YangMills coupled to biadjoint scalars  which we implement via oneloop CachazoHeYuan formulae. The YM+phi^3 building blocks are obtained from forward limits of treelevel input in external gluons and scalars, and we give the composition rules for any number of traces and orders in the couplings g and kappa. One the one hand, we spell out supersymmetry and dimensionagnostic relations that reduce loop integrands of EinsteinYangMills to those of pure gauge theories. On the other hand, we present fourpoint results for maximal and halfmaximal supersymmetry where all supersymmetry cancellations are exposed. In the halfmaximal case, we determine sixdimensional anomalies due to chiral hypermultiplets in the loop.

Gravitational waves in dark bubble cosmology
Authors: Ulf Danielsson, Daniel Panizo and Rob Tielemans
Preprint number: UUITP03/22
Abstract: In this paper we construct the 5D uplift of 4D gravitational waves in de Sitter cosmology for the brane world scenario based on a nucleated bubble in AdS5. This makes it possible to generalize the connection between the dark bubbles and Vilenkin's quantum cosmology to include gravitational perturbations. We also use the uplift to explain the interpretation of the apparently negative energy contributions in the 4D Einstein equations, which distinguish the dark bubble scenario from RandallSundrum.

Vanishing Yukawa Couplings and the Geometry of String Theory Models
Authors: L. B. Anderson, J. Gray, M. Larfors, M. Magill
Preprint number: UUITP02/22
Abstract: We provide an overview of recent work which aims to understand patterns of vanishing Yukawa couplings that arise in models of particle physics derived from string theory. These patterns are seemingly linked to a plethora of different geometrical structures and our understanding of the subject has yet to be consolidated in a unified framework. This short note is based upon a talk that was given by one of the authors at the Nankai Symposium on Mathematical Dialogues. Therefore it is aimed at a mathematical audience of mixed academic background.

Higher Symmetries of 5d Orbifold SCFTs
Authors: Michele Del Zotto, Jonathan J. Heckman, Shani Nadir Meynet, Robert Moscrop, Hao Y. Zhang
Preprint number: UUITP01/22
Abstract: We determine the higher symmetries of 5d SCFTs engineered from Mtheory on a C^{3}/Γ background for Γ a finite subgroup of SU(3). This resolves a longstanding question as to how to extract this data when the resulting singularity is nontoric (when Γ is nonabelian) and/or not isolated (when the action of Γ has fixed loci). The BPS states of the theory are encoded in a 1D quiver quantum mechanics gauge theory which determines the possible 1form and 2form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0form symmetry, the abelianization of Γ detects a 2group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.
Preprints 2021

Evaluation of multiloop multiscale Feynman integrals for precision physics
Authors: Ievgen Dubovyk, Ayres Freitas, Janusz Gluza, Krzysztof Grzanka, Martijn Hidding, and Johann Usovitsch
Preprint number: UUITP66/21
Abstract: Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders will require threeloop electroweak and mixed electroweakQCD corrections to singleparticle production and decay processes and twoloop electroweak corrections to pair production processes, all of which are beyond the reach of existing analytical and numerical techniques in their current form. This article presents a new seminumerical approach based on differential equations with boundary terms specified at Euclidean kinematic points. These Euclidean boundary terms can be computed numerically with high accuracy using sector decomposition or other numerical methods. They are then mapped to the physical kinematic configuration with a series solution of the differential equation system. The method is able to deliver 8 or more digits precision, and it has a builtin mechanism for checking the accuracy of the obtained results. Its efficacy is illustrated with examples for threeloop selfenergy and vertex integrals and twoloop box integrals. 
OPE coefficients in ArgyresDouglas theories
Authors: Agnese Bissi, Francesco Fucito, Andrea Manenti, Francisco Morales, Raffaele Savelli
Preprint number: UUITP65/21
Abstract: The calculation of physical quantities in certain quantum field theories such as those of the ArgyresDouglas type is notoriously hard, due to the lack of a Lagrangian description. Here we tackle this problem following two alternative approaches. On the one hand, we use localization on the foursphere to compute twocorrelators and OPE coefficients in ArgyresDouglas superconformal theories. On the other hand, we use the conformal bootstrap machinery to put stringent bounds on such coefficients, only relying on the knowledge of central charge and conformal dimension of the operators. We compare the results obtained with these two methods and find good agreement for all rankone cases and for the ranktwo ArgyresDouglas theories $(A_1,A_4)$ and $(A_1,A_5)$, in the moduli space of pure $SU(5)$ and $SU(6)$ super YangMills. We also apply our results from localization to obtain bounds on the dimensions of the lightest neutral unprotected operators of the CFTs.

Index of the Transversally Elliptic Complex from N=2 Localization in Four Dimensions
Authors: Roman Mauch and Lorenzo Ruggeri
Preprint number: UUITP64/21
Abstract: We present a formula for the equivariant index of the cohomological complex
obtained from localization of N = 2 SYM on simplyconnected compact fourmanifolds
with a T2action. When the theory is topologically twisted, the complex is elliptic and
its index can be computed in a standard way using the AtiyahBott localization formula.
Recently, a framework for more general types of twisting, socalled cohomological twisting,
was introduced for which the complex turns out only to be transversally elliptic. While the
index of such a complex was previously computed for specific manifolds and a systematic
procedure for its computation was provided for cases where the manifold can be lifted to
a Sasakian S1fibration in five dimensions, a purely fourdimensional treatment was still
lacking. In this note, we provide a formal treatment of the cohomological complex, showing
that the Laplacian part can be globally split off while the remaining part can be trivialized
in the groupdirection. This ultimately produces a simple formula for the index applicable
for any compact simplyconnected fourmanifold, from which one can easily compute the
perturbative partition function. 
OffShell ColorKinematics Duality for ChernSimons
Authors: Maor BenShahar, Henrik Johansson
Preprint number: UUITP63/21
Abstract: Many gauge theories possess a hidden duality between color and kinematics in their onshell scattering amplitudes. An open problem is to formulate an offshell realization of the duality, thus manifesting a kinematic algebra. We show that 3D ChernSimons (CS) theory in Lorenz gauge obeys offshell colorkinematics duality. This holds both for the gauge field and the BRST ghosts, and the duality is manifest in the Feynman rules. A kinematic algebra can be formulated through a secondorder differential operator (Poisson bracket) acting on the offshell fields, and it corresponds to 3D diffeomorphisms generated by functions in Lorenz gauge. We consider several admissible doublecopy constructions of CS theory with YangMills theory, a higherderivative (DF)^2 gauge theory, or CS theory itself. To obtain nonvanishing amplitudes, we deform pure CS theory by including the maximum amount of adjoint matter that respect the onshell duality. This gives a new formulation of a N=4 CSmatter theory, with fields of unusual statistics. We argue that the colorstripped tree amplitudes of this theory are equivalent to those of the GaiottoWitten N=4 CS theory with bifundamental matter. We further show that the double copy of the N=4 CS theory with itself corresponds to maximally supersymmetric N=8 DiracBornInfeld theory.

Maximal SuperYangMills at Six Loops via Novel Integrand Bootstrap
Authors: John Joseph Carrasco, Alexander Edison, Henrik Johansson
Preprint number: UUITP62/21
Abstract: We construct the complete (planar and nonplanar) integrand for the sixloop fourpoint amplitude in maximal D=<10 superYangMills. This construction employs new advances that combat the proliferation of diagram contributions and state sums when evaluating multiloop Ddimensional unitarity cuts. Concretely, we introduce two graphbased approaches to evaluating generalized unitarity cuts in D dimensions: 1) recursively from lowerloop cuts, or 2) directly from known higherloop planar cuts. Neither method relies on explicit state sums or any sewing of treelevel amplitudes. These methods are based on identities that we expect to hold for a broad family of theories, including QCD and Einstein gravity.

Quadraticinspin interactions at the fifth postNewtonian order probe new physics
Authors: JungWook Kim, Michèle Levi, Zhewei Yin
Preprint number: UUITP61/21
Abstract: We derive the observable binding energies and their relations to the angular momentum for the nexttonexttonexttoleading order (N^3LO) of all quadraticinspin interactions in postNewtonian (PN) gravity. Our results are valid for all generic compact binaries, and enter at the fifth PN order for maximallyrotating compact objects, thus pushing the state of the art. This is accomplished through an extension of the effective field theory of spinning gravitating objects. We find a new operator that contributes to the observables, making the associated Wilson coefficient a new probe for candidate theories of gravity and for QCD.

Kinematic Hopf Algebra for BCJ Numerators in HeavyMass Effective Field Theory and Yang–Mills Theory
Authors: Andreas Brandhuber, Gang Chen, Henrik Johansson, Gabriele Travaglini and Congkao Wen
Preprint Number: UUITP60/21
Abstract: We present a closed formula for all BCJ numerators describing Ddimensional treelevel scattering amplitudes in a heavymass effective field theory with two massive particles and an arbitrary number of gluons. The corresponding gravitational amplitudes obtained via the double copy directly enter the computation of blackhole scattering and gravitationalwave emission. Our construction is based on finding a kinematic algebra for the numerators, which we relate to a quasishuffle Hopf algebra. The BCJ numerators thus obtained have a compact form and intriguing features: gauge invariance is manifest, locality is respected for massless exchange, and they contain poles corresponding to massive exchange. Counting the number of terms in a BCJ numerator for n2 gluons gives the Fubini numbers F_{n3} reflecting the underlying quasishuffle Hopf algebra structure. Finally, by considering an appropriate factorisation limit, the massive particles decouple, and we thus obtain a kinematic algebra and all treelevel BCJ numerators for Ddimensional pure YangMills theory.

The gluon Regge trajectory at three loops from planar YangMills theory
Authors: Vittorio Del Duca, Robin Marzucca, Bram Verbeek
Preprint Number: UUIPT59/21
Abstract: We compute the threeloop leadingcolour corrections to the YangMills Regge trajectory and gluon impact factor. Conjecturing that, in analogy with N=4 super YangMills (SYM), in a suitable scheme Ncsubleading terms are absent from the threeloop Regge trajectory, we understand our result as the first computation of the pure gauge, or nf = 0, part of the QCD threeloop Regge trajectory. The results are presented both for the bare and renormalised amplitudes and are consistent with predictions from infrared factorisation along with reproducing known results in planar N=4 SYM through a maximal weight truncation. We also include the dependence on a Regge factorisation scale to facilitate future applications in BFKL theory at nexttonextto leading logarithmic accuracy.

Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
Authors: Adam Chalabi, Christopher P. Herzog, Andy O'Bannon, Brandon Robinson, Jacopo Sisti
Preprint number: UUITP58/21
Abstract: Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension d ≥ 5 with a conformallyinvariant spatial boundary (BCFTs) or 4dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing WessZumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT's Weyl tensor. For a codimension one boundary or defect (i.e. d=5), we reproduce the 9 parityeven terms found by Astaneh and Solodukhin, and we discover 3 parityodd terms. For larger codimension, we find 23 parityeven terms and 6 parityodd terms. The coefficient of each term defines a "central charge'' that characterizes the BCFT or DCFT. We show how several of the parityeven central charges enter physical observables, namely the displacement operator twopoint function, the stresstensor onepoint function, and the universal part of the entanglement entropy. We compute several parityeven central charges in tractable examples: monodromy and conical defects of free, massless scalars and Dirac fermions in d=6; probe branes in Antide Sitter (AdS) space dual to defects in CFTs with d ≥ 6; and Takayanagi's AdS/BCFT with d=5. We demonstrate that several of our examples obey the boundary/defect atheorem, as expected.

Shifts of prepotentials
Authors: N. Nekrasov, N. Piazzalunga, M. Zabzine
Preprint number: UUITP57/21
Abstract: We study the dynamics of supersymmetric theories in five dimensions obtained by compactifications of Mtheory on a CalabiYau threefold X. For a compact X, this is determined by the geometry of X, in particular the Kahler class dependence of the volume of X determines the effective couplings of vector multiplets. Rigid supersymmetry emerges in the limit of divergent volume, prompting the study of the structure of DuistermaatHeckman formula and its generalizations for noncompact toric Kahler manifolds. Our main tool is the set of finitedifference equations obeyed by equivariant volumes and their quantum versions. We also discuss a physical application of these equations in the context of sevendimensional gauge theories, extending and clarifying our previous results.

Ftheory on 6D Symmetric Toroidal Orbifolds
Authors: Finn Bjarne Kohl, Magdalena Larfors and PaulKonstantin Oehlmann
Preprint number: UUITP56/21
Abstract: In this work we study Ftheory on symmetric toroidal orbifolds that exhibit rototranslations, which are point group rotations accompanied by fractional lattice shifts. These geometries admit a rich class of effects, such as twisted affine folded fibers, multiple fibers, and up to three distinct torusfibrations that yield different M/Ftheory lifts. We discuss the sixdimensional physics of the Ftheory lifts, which generically host superconformal subsectors and a IIB axiodilaton fixed to strong coupling. In addition we find that these theories exhibit a rich set of $p=0,1,2$ discrete $p$form gauge symmetries. We discuss sixdimensional gauge and supergravity anomalies and match the rank and tensor branch dimension to the Hodge numbers that were computed using heterotic world sheet techniques.

Rebooting quarterBPS operators in N = 4 Super YangMills
Authors: Agnese Bissi, Giulia Fardelli, Andrea Manenti
Preprint number: UUITP55/21
Abstract: We start a systematic study of quarterBPS operators in fourdimensional N = 4 Super YangMills with gauge group SU(N) making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing Rsymmetry tensor structures, and we use the underlined chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the fourpoint correlators, up to few ambiguities. As applications, we use the Lorentzian inversion formula to study the leading order OPE data in the large N supergravity limit and we make contact with the OPE limit of the fivepoint function of halfBPS operators.

Nijenhuis tensor and invariant polynomials
Authors: F. Bonechi, J. Qiu, M. Tarlini, E. Viviani
Preprint number: UUITP54/21
Abstract: We discuss the diagonalization problem of the Nijenhuis tensor in a class of {\it PoissonNijenhuis} structures defined on compact hermitian symmetric spaces. We study its action on the ring of invariant polynomials of a Thimm chain of subalgebras. The existence of $\phi${\it minimal representations} defines a suitable basis of invariant polynomials that completely solves the diagonalization problem. We prove that such reprentations exist in the classical cases AIII, BDI, DIII and CI, and do not exist in the exceptional cases EIII and EVII. We discuss a second general construction that in these two cases computes partially the spectrum and hints at a different behavior with respect to the classical cases.

Learning Size and Shape of CalabiYau Spaces
Authors: Magdalena Larfors, Andre Lukas, Fabian Ruehle, Robin Schneider
Preprint number: UUITP53/21
Abstract: We present a new machine learning library for computing metrics of string
compactification spaces. We benchmark the performance on MonteCarlo sampled
integrals against previous numerical approximations and find that our neural
networks are more sample and computationefficient. We are the first to
provide the possibility to compute these metrics for arbitrary, userspecified
shape and size parameters of the compact space and observe a linear relation
between optimization of the partial differential equation we are training
against and vanishing Ricci curvature. 
SYM on Quotients of Spheres and Complex Projective Spaces
Authors: Jim Lundin and Lorenzo Ruggeri
Preprint number: UUITP52/21
Abstract: We introduce a generic procedure to reduce a supersymmetric YangMills (SYM) theory along the Hopf fiber of squashed $S^{2r1}$ with $U(1)^r$ isometry, down to the $\mathbb{CP}^{r1}$ base. This amounts to fixing a Killing vector $v$ generating a $U(1)\subset U(1)^r$ rotation and dimensionally reducing either along $v$ or along another direction contained in $U(1)^r$. To perform such reduction we introduce a $\mathbb{Z}_p$ quotient freely acting along one of the two fibers. For fixed $p$ the resulting manifolds $S^{2r1}/\mathbb{Z}_p\equiv L^{2r1}(p,\pm 1)$ are a higher dimensional generalization of lens spaces. In the large $p$ limit the fiber shrinks and effectively we find theories living on the base manifold. Starting from $\mathcal{N}=2$ SYM on $S^3$ and $\mathcal{N}=1$ SYM on $S^5$ we compute the partition functions on $L^{2r1}(p,\pm 1)$ and, in the large $p$ limit, on $\mathbb{CP}^{r1}$, respectively for $r=2$ and $r=3$. We show how the reductions along the two inequivalent fibers give rise to two distinct theories on the base. Reducing along $v$ gives an equivariant version of DonaldsonWitten theory while the other choice leads to a supersymmetric theory closely related to Pestun's theory on $S^4$. We use our technique to reproduce known results for $r=2$ and we provide new results for $r=3$. In particular we show how, at large $p$, the sum over fluxes on $\mathbb{CP}^2$ arises from a sum over flat connections on $L^{5}(p,\pm 1)$. Finally, for $r=3$, we also comment on the factorization of perturbative partition functions on non simply connected manifolds.

Oneloop Gluon Amplitudes in AdS
Authors: Luis F. Alday, Agnese Bissi, Xinan Zhou
Preprint number: UUITP51/21

Flavor deformations and supersymmetry enhancement in $4d\ \NN=2$ theories
Authors: Usman Naseer and Charles Thull
Preprint number: UUITP50/21
Abstract: We study $\NN=2$ theories on fourdimensional manifolds that admit a Killing vector $v$ with isolated fixed points. It is possible to deform these theories by coupling positiondependent background fields to the flavor current multiplet. The partition function of the deformed theory only depends on the value of the background scalar fields at the fixed points of $v$. For a single adjoint hypermultiplet, the partition function becomes independent of the supergravity as well as the flavor background if the scalars attain special values at the fixed points. For these special values, supersymmetry at the fixed points enhances from the DonaldsonWitten twist to the Marcus twist or the VafaWitten twist of $\NN=4$ SYM. Our results explain the recently observed squashing independence of $\NN=2^*$ theory on the squashed sphere and provide a new squashing independent point. Interpreted through the AGTcorrespondence, this implies the $b$independence of torus onepoint functions of certain \emph{local} operators in Liouville/Toda CFT. The positiondependent deformations imply relations between correlators of partially integrated operators in \emph{any} $\NN=2$ SCFT with flavor symmetries.

Reexamining the stability of rotating horizonless black shells mimicking Kerr black holes
Authors: Ulf Danielsson, Suvendu Giri
Preprint number: UUITP49/21
Abstract: In arXiv:1705.10172 a string theory inspired alternative to gravitational collapse was proposed, consisting of a bubble of AdS space made up of ingredients from string theory. These ultra compact objects are 9/8 times the size of the corresponding Schwarzschild black hole, but being within the photosphere are almost indistinguishable from them. Slowly rotating counterparts of these black shells were constructed in arXiv:1712.00511, which closely mimic a Kerr black hole, but have a quadrupole moment that differs from Kerr. Recently, arXiv:2109.09814 studied the dynamicalstability of the stationary black shells against radial perturbations and accretion of matter, andexamined a two parameter family of fluxes required for stability. In this paper, we reexamine therotating black shells with particular attention to the constraints imposed by this dynamical analysisfor nonrotating shells. Extrapolating these results to rotating shells, we find that they can indeedsupport themselves at a critical point in the gravitational potential. Additionally, requiring that theysettle back to their new Buchdahl radius after accreting matter, uniquely fixes the fluxes required fordynamical stability. The flux parameters turn out to have an extremely simple form, and fulfil oneof the constraints for perturbative radial stability while exactly saturating the other. The preferredquadrupole moment that we find, given some physical assumptions, is 7% less than Kerr.

KillingYano Cotton Currents
Authors: Ulf Lindström and Özgür Sariıoğlu
Preprint number: UUITP48/21
Abstract: We discuss conserved currents constructed from the Cotton tensor and (conformal) KillingYano tensors. We consider the corresponding charges generally and then exemplify with the fourdimensional Pleban ́skiDemian ́ski metric where they are proportional to the sum of the squares of the electric and the magnetic charges. As part of the derivation, we also find the two conformal KillingYano tensors of the Pleban ́skiDemian ́ski metric in the recently introduced coordinates of Podolsky and Vratny. The construction of asymptotic charges for the Cotton current is elucidated and compared to the threedimensional construction in Topologically Massive Gravity. For the threedimensional case, we also give a conformal superspace multiplet that contains the Cotton current in the bosonic sector. In a mathematical section, we derive potentials for the currents, find identities for conformal KYTs and for KYTs in torsionful backgrounds. 
Manifest colourkinematics duality and double copy in the stringinspired formalism
Authors: Naser Ahmadiniaz, Filippo Maria Balli, Olindo Corradini, Cristhiam LopezArcos, Alexander Quintero Vélez, Christian Schubert
Preprint number: UUITP47/21
Abstract: The relation for the gravity polarisation as the tensor product of two gluon polarisation vectors has been wellknown for a long time, but a version of this relation for multiparticle fields is still not present. Here we show that in order for this to happen we first have to ensure that the multiparticle polarisations satisfy colourkinematics duality, which arises naturally from the BernKosower formalism for oneloop gluon amplitudes, and later we will see that the tensor product for multiparticle fields arises naturally in the Bern DunbarShimada formalism for oneloop gravity amplitudes. This allows us to formulate a new prescription for doublecopy gravity BerendsGiele currents that can be applied to other cases. To make this point we also present other examples.

Double parton distributions out of bounds in colour space
Authors: Markus Diehl, Jonathan R. Gaunt, Paolo Pichini and Peter Ploessl
Preprint number: UUITP46/21
Abstract: We investigate the positivity of double parton distributions with a nontrivial dependence on the parton colour. It turns out that positivity is not preserved by leadingorder evolution from lower to higher scales, in contrast to the case in which parton colour is summed over. We also study the positivity properties of the distributions at small distance between the two partons, where they can be computed in terms of perturbative splitting kernels and ordinary parton densities.

Phases of N=1 Quivers in 2+1 Dimensions
Authors: Vladimir Bashmakov, Nicola Gorini
Preprint number: UUITP45/21
Abstract: We consider the IR phases of twonode quiver theories with N=1 supersymmetry in d=2+1 dimensions. It turns out that the discussion splits into two main cases, depending on whether the ChernSimons levels associated with two nodes have the same sign, or the opposite signs, with the latter case being more nontrivial. The determination of the phase diagrams allows us to conjecture certain infrared dualities involving either two quiver theories, or a quiver and adjoint QCD. We also provide a short discussion of quivers possessing time reversal symmetry.

Monodromy Bootstrap for SU(22) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
Authors: Simon Ekhammar, Dmytro Volin
Preprint number: UUITP44/21
Abstract: We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new systems. Two are based on SU(22) symmetry, and we show that one of them describes Hubbard model. Two more are based on SU(22)xSU(22). In the special subcase of PSU(1,12)xPSU(1,12) we get the unique nontrivial option and hence it is a natural candidate for the quantum spectral curve for AdS3/CFT2 integrability for AdS3xS3xS3xT4 background supported by RRflux.

P1fibrations in Ftheory and String Dualities
Authors: Lara B. Anderson, James Gray, Mohsen Karkheiran, PaulKonstantin
Oehlmann and Nikhil RaghuramPreprint number: UUITP43/21
Abstract: In this work we study Ftheory compactifications on elliptically fibered
CalabiYau nfolds which have $\mathbb{P}^1$fibered base manifolds. Such
geometries, which we study in both 4 and 6dimensions, are both ubiquitous
within the set of CalabiYau manifolds and play a crucial role in
heterotic/Ftheory duality. We discuss the most general formulation of
$\mathbb{P}^1$bundles of this type, as well as fibrations which degenerate at
higher codimension loci. In the course of this study, we find a number of new
phenomena. For example, in both 4 and 6dimensions we find transitions whereby
the base of a $\mathbb{P}^1$bundle can change nature, or "jump", at certain
loci in complex structure moduli space. We discuss the implications of this
jumping for the associated heterotic duals. We argue that
$\mathbb{P}^1$bundles with only rational sections lead to heterotic duals
where the CalabiYau manifold is elliptically fibered over the section of the
$\mathbb{P}^1$ bundle, and not its base. As expected, we see that
degenerations of the $\mathbb{P}^1$fibration of the Ftheory base correspond
to 5branes in the dual heterotic physics, with the exception of cases in which
the fiber degenerations exhibit monodromy. Along the way, we discuss a set of
useful formulae and tools for describing Ftheory compactifications on this
class of CalabiYau manifolds. 
Poincaré series for modular graph forms at depth two II. Iterated integrals of cusp forms
Authors: Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer
Preprint number: UUITP42/21
Abstract: We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincaré series in a companion paper. The source term of the Laplace equation is a product of (derivatives of) two nonholomorphic Eisenstein series whence the modular invariants are assigned depth two. These modular invariant functions can sometimes be expressed in terms of singlevalued iterated integrals of holomorphic Eisenstein series as they appear in generating series of modular graph forms. We show that the set of iterated integrals of Eisenstein series has to be extended to include also iterated integrals of holomorphic cusp forms to find expressions for all modular invariant functions of depth two. The coefficients of these cusp forms are identified as ratios of their Lvalues inside and outside the critical strip.

Poincaré series for modular graph forms at depth two I: Seeds and Laplace systems
Authors: Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer
Preprint number: UUITP41/21
Abstract: We derive new Poincaréseries representations for infinite families of nonholomorphic modular invariant functions that include modular graph forms as they appear in the lowenergy expansion of closedstring scattering amplitudes at genus one. The Poincaré series are constructed from iterated integrals over single holomorphic Eisenstein series and their complex conjugates, decorated by suitable combinations of zeta values. We evaluate the Poincaré sums over these iterated Eisenstein integrals of depth one and deduce new representations for all modular graph forms built from iterated Eisenstein integrals at depth two. In a companion paper, some of the Poincaré sums over depthone integrals going beyond modular graph forms will be described in terms of iterated integrals over holomorphic cusp forms and their Lvalues.

Evidence for an Algebra of G2 Instantons
Authors: Michele Del Zotto, Jihwan Oh, Yehao Zhou
Preprint number: UUITP40/21
Abstract: In this short note, we present some evidence towards the existence of an algebra of BPS G_{2} instantons. These are instantonic configurations that govern the partition functions of 7d SYM theories on local G_{2} holonomy manifolds X. To shed light on such structure, we begin investigating the relation with parent 4d N=1 theories obtained by geometric engineering Mtheory on X. The main point of this paper is to substantiate the following dream: the holomorphic sector of such theories on multicentered TaubNUT spaces gives rise to an algebra whose characters organise the G_{2} instanton partition function. As a first step towards this program, we argue by string duality that a multitude of geometries X exist that are dual to wellknown 4d SCFTs arising from D3 branes probes of CY cones: all these models are amenable to analysis along the lines suggested by Dijkgraaf, Gukov, Neitzke and Vafa in the context of topological Mtheory. Moreover, we discuss an interesting relation to Costello's twisted Mtheory, which arises at local patches, and is a key ingredient in identifying the relevant algebras.

The Characteristic Dimension of Fourdimensional N=2 SCFTs
Authors: Sergio Cecotti, Michele Del Zotto, Mario Martone, and Robert Moscrop
Preprint: UUITP39/21Abstract: In this paper we introduce the characteristic dimension of a four dimensional N=2 superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We prove that only nine values of the characteristic dimension are allowed, −∞, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving a new organizing principle to the vast landscape of 4d N=2 SCFTs. Whenever the characteristic dimension differs from 1 or 2, only very constrained special Kähler geometries (i.e. isotrivial, diagonal and rigid) are compatible with the corresponding set of Coulomb branch dimensions and extremely special, maximally strongly coupled, BPS spectra are allowed for the theories which realize them. Our discussion applies to superconformal field theories of arbitrary rank, i.e. with Coulomb branches of any complex dimension. Along the way, we predict the existence of new N=3 theories of rank two with nontrivial oneform symmetries.

GreenSchwarz and Pure Spinor Formulations of Chiral Strings
Author: Max Guillen
Preprint number: UUITP38/21
Abstract: Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the GreenSchwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a lightcone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the OdaTonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.

10D SuperYangMills Scattering Amplitudes From Its Pure Spinor Action
Authors: Maor BenShahar and Max Guillen
Preprint number: UUITP37/21
Abstract: Using the pure spinor master action for 10D superYangMills in the gauge $b_{0}V = Q\Xi$, treelevel scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested $b$ghost operators, and show that the Siegel gauge condition $b_{0}V = 0$ gives rise to colorkinematics duality satisfying numerators whose Jacobi identity follows from that of a kinematic algebra.

Deep multitask mining CalabiYau fourfolds
Authors: Harold Erbin, Riccardo Finotello, Robin Schneider and Mohamed Tamaazousti
Preprint number: UUITP36/21
Abstract: We continue earlier efforts in computing the dimensions of tangent space cohomologies of CalabiYau manifolds using deep learning. In this paper, we consider the dataset of all CalabiYau fourfolds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by stateoftheart computer vision architectures, we improve earlier benchmarks and demonstrate that all four nontrivial Hodge numbers can be learned at the same time using a multitask architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for $h^{(1,1)}$ and 97% for $h^{(2,1)}$ (100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for $h^{(2,2)}$. Assuming that the Euler number is known (since it is easy to compute) and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

Twoloop superstring fivepoint amplitudes III, construction via the RNS formulation: even spin structures
Authors: Eric D'Hoker and Oliver Schlotterer
Preprint number: UUITP35/21
Abstract: The contribution from even spin structures to the genustwo amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genustwo amplitude with four external NS states. The results agree with the parityeven NS components of a construction using chiral splitting and pure spinors given in earlier companion papers arXiv:2006.05270 and arXiv:2008.08687.

Compton BlackHole Scattering for s ≤ 5/2
Authors: Marco Chiodaroli, Henrik Johansson and Paolo Pichini
Preprint number: UUITP34/21
Abstract: Quantum scattering amplitudes for massive matter have received new attention in connection to classical calculations relevant to gravitationalwave physics. Amplitude methods and insights are now employed for precision computations of observables needed for describing the gravitational dynamics of bound massive objects such as black holes. An important direction is the inclusion of spin effects needed to accurately describe rotating (Kerr) black holes. Higherspin amplitudes introduced by ArkaniHamed, Huang and Huang at three points have by now a firm connection to the effective description of Kerr blackhole physics. The corresponding Compton higherspin amplitudes remain however an elusive open problem. Here we draw from results of the higherspin literature and show that physical insights can be used to uniquely fix the Compton amplitudes up to spin 5/2, by imposing a constraint on a threepoint higherspin current that is a necessary condition for the existence of an underlying unitary theory. We give the unique effective Lagrangians up to spin 5/2, and show that they reproduce the previouslyknown amplitudes. For the multigraviton amplitudes analogous to the Compton amplitude, no further corrections to our Lagrangians are expected, and hence such amplitudes are uniquely predicted. As an essential tool, we introduce a modified version of the massive spinorhelicity formalism which allows us to conveniently obtain higherspin states, propagators and compact expressions for the amplitudes

Two applications of the analytic conformal bootstrap: A quick tour guide
Authors: Agnese Bissi, Parijat Dey and Giulia Fardelli
Preprint number: UUITP33/21
Abstract: We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular in the analytic structure and in the associativity of the operator product expansion. We focus on two applications of the analytic conformal bootstrap: the study of the $\epsilon$ expansion of the Wilson Fisher model via the introduction of a dispersion relation and the large $N$ expansion of maximally supersymmetric Super Yang Mills theory in four dimensions.

On refined ChernSimons and refined ABJ matrix models
Authors: Luca Cassia and Maxim Zabzine
Preprint number: UUITP32/21
Abstract: We consider the matrix model of U(N) refined ChernSimons theory on S³ for the unknot. We derive a qdifference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as qVirasoro constraints. The constraints are rewritten as difference equations for the generating function of Wilson loop expectation values which we solve as a recursion for the correlators of the model. The solution is repackaged in the form of superintegrability formulas for Macdonald polynomials. Additionally, we derive an equivalent qdifference operator for a similar refinement of ABJ theory and show that the corresponding qVirasoro constraints are equal to those of refined ChernSimons for a gauge supergroup U(NM). Our equations and solutions are manifestly symmetric under Langlands duality q ↔ 1/t which correctly reproduces 3d Seiberg duality when q is a specific root of unity.

Oneloop matrix elements of effective superstring interactions: alpha'expanding loop integrands
Authors: Alex Edison, Max Guillen, Henrik Johansson, Oliver Schlotterer and Fei Teng
Preprint number: UUITP31/21
Abstract: In the lowenergy effective action of string theories, nonabelian gauge interactions and supergravity are augmented by infinite towers of highermassdimension operators. We propose a new method to construct oneloop matrix elements with insertions of operators D^{2k} F^n and D^{2k} R^n in the treelevel effective action of typeI and typeII superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of modulispace integrals using string treelevel amplitudes with two extra points, expanded in powers of the inverse string tension alpha'. Similar to oneloop ambitwistor computations, intermediate steps feature nonstandard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey oneloop versions of the monodromy and KLT relations. We express a variety of four and fivepoint examples in terms of quadratic propagators and formulate a criterion on the underlying genusone correlation functions that should make this recombination possible at all orders in alpha'. The ultraviolet divergences of the oneloop matrix elements are crosschecked against the nonseparating degeneration of genusone integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

Squashing and supersymmetry enhancement in three dimensions
Authors: Joseph Minahan, Usman Naseer and Charles Thull
Preprint number: UUITP30/21
We consider massdeformed theories with ${\cal N}\geq2$ supersymmetry on round and squashed threespheres. By embedding the supersymmetric backgrounds in extended supergravity we show that at special values of mass deformations the supersymmetry is enhanced on the squashed spheres. When the $3d$ partition function can be obtained by a limit of a $4d$ index we also show that for these special mass deformations only the states annihilated by extra supercharges contribute to the index. By using an equivalence between partition functions on squashed spheres and ellipsoids, we explain the recently observed squashing independence of the partition function of massdeformed ABJM theory on the ellipsoid. We provide further examples of such simplification for various $3d$ supersymmetric theories.

Scaleseparated AdS$_4$ vacua of IIA orientifolds and Mtheory
Authors: N. Cribiori, D. Junghans, V. Van Hemelryck, T. Van Riet, T. Wrase
Preprint number: UUITP29/21
Abstract: We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and Mtheory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scaleseparated and sourceless (but classically singular) geometries in 11D supergravity.

Gauged 2form Symmetries in 6D SCFTs Coupled to Gravity
Authors: Andreas P. Braun, PaulKonstantin Oehlmann, and Magdalena Larfors
Preprint number: UUITP28/21
Abstract: We study six dimensional supergravity theories with superconformal sectors(SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally FTheory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2form global symmetries of the SCFT sectors. For both $(2,0)$ and $(1,0)$ theories we show that whenever the charge lattice of the SCFT sectors is nonprimitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2form symmetry embeds into the 2form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.

Bulk reconstruction and Bogoliubov transformations in AdS$_2$
Authors: Parijat Dey and Nirmalya Kajuri
Preprint number: UUITP27/21
Abstract: In the bulk reconstruction program, one constructs boundary representations of bulk fields. However, the boundary representations derived in global and AdSRindler coordinates appear to be inequivalent as the AdSRindler smearing function is known to diverge in dimensions greater than two. This is an apparent paradox. We investigate the relation between the two representations for AdS$_2$. We obtain the AdSRindler smearing function for massive and massless fields and show that the global and AdSRindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdSRindler modes for both massive and massless particles.

The FL bound and its phenomenological implications
Authors: Miguel Montero, Cumrun Vafa, Thomas Van Riet and Gerben Venken
Preprint number: UUITP26/21
Abstract: Demanding that charged Nariai black holes in (quasi)de Sitter space decay
without becoming superextremal implies a lower bound on the masses of charged particles, known as the Festina Lente (FL) bound. In this paper we elucidate various aspects of this bound as well as extensions of it to d > 4 and to situations with scalar potentials and dilatonic couplings. We also discuss phenomenological implications of FL including an explanation of why the Higgs potential cannot have a local minimum at the origin, thus explaining why the weak force must be broken. For constructions of metastable dS involving antibrane uplift scenarios, even though the throat region is consistent with FL, the bound implies that we cannot have any light charged matter elds coming from any far away region in the compactified geometry, contrary to the fact that they are typically expected to arise in these scenarios. This strongly suggests that introduction of warped antibranes in the throat cannot be decoupled from the bulk dynamics as is commonly assumed. Finally, we provide some evidence that in certain situations the FL bound can have implications even with gravity decoupled and illustrate this in the context of noncompact throats. 
Nonperturbative effects and resurgence in JT gravity at finite cutoff
Authors: Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara
Preprint number: UUITP25/21
Abstract: We investigate the nonperturbative structure of JackiwTeitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a TTdeformed Schwarzian quantum mechanics. Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. We show that the perturbative series is asymptotic and that it admits a precise completion exploiting the analytical properties of its Borel transform, as prescribed by resurgence theory. The final result is then naturally interpreted in terms of the nonperturbative branch of the TTdeformed spectrum. The finitecutoff trumpet partition function is computed by applying the same strategy. In the second part of the paper, we propose an extension of this formalism to arbitrary topologies, using the basic gluing rules of the undeformed case. The WeilPetersson integrations can be safely performed due to the nonperturbative corrections and give results that are compatible with the flow equation associated with the TT deformation. We derive exact expressions for general topologies and show that these are captured by a suitable deformation of the EynardOrantin topological recursion. Finally, we study the "slope" and "ramp" regimes of the spectral form factor as functions of the cutoff parameter.

On the squashed sevensphere operator spectrum
Authors: S. Ekhammar, B. E. W. Nilsson
Preprint number: UUITP24/21
Abstract: We derive major parts of the eigenvalue spectrum of the operators on the squashed sevensphere that appear in the compactification of elevendimensional supergravity. These spectra determine the mass spectrum of the fields in AdS_{4} and are important for the corresponding N =1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS_{4} was derived for this compactification. Some comments are also made concerning the G_{2} holonomy and its implications on the structure of the operator equations on the squashed sevensphere.

Infrared Divergences and the Eikonal
Authors: Carlo Heissenberg
Preprint number: UUITP23/21
Abstract: The aim of this note is to explore the interplay between the eikonal resummation in impactparameter space and the exponentiation of infrared divergences in momentum space for gravity amplitudes describing collisions of massive objects. The eikonal governs the classical dynamics relevant to the twobody problem, and its infrared properties are directly linked to the zero frequency limit of the gravitational wave emission spectrum and to radiation reaction effects. Combining eikonal and infrared exponentiations it is possible to derive these properties at a given loop order starting from lowerloop data. This is illustrated explicitly in N = 8 supergravity and in general relativity by deriving the divergent part of the twoloop eikonal from treelevel and oneloop elastic amplitudes.

A higherdimensional view on quantum cosmology
Authors: U. H. Danielsson, D. Panizo, R. Tielemans, T. Van Riet
Preprint number: UUITP22/21
Abstract: We argue that the choice of boundary condition for the wavefunction in quantum cosmology depends on the UV completion of general relativity. We provide an explicit example using a braneworld scenario in which a de Sitter cosmology is induced on the surface of a CDL bubble in a 5dimensional AdS space. The corresponding boundary conditions are unambigously fixed by demanding consistency with the known physics of bubble nucleation and this selects the Vilenkin choice from a 4D viewpoint.

NexttoMHV YangMills kinematic algebra
Authors: Gang Chen, Henrik Johansson, Fei Teng and Tianheng Wang
Preprint number: UUITP21/21
Abstract: Kinematic numerators of YangMills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinitedimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in YangMills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closedform expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.

New currents with KillingYano tensors
Authors: Ulf Lindström and Özgür Sarioglu
Preprint number: UUITP20/21
Abstract: New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit KillingYano tensors are described. These relations are then used to introduce novel conserved currents involving such KillingYano tensors. For a particular current based on the Einstein tensor, we discuss the issue of conserved charges and consider implications for the matter coupling to gravity. The condition on the background geometry to allow asymptotic conserved charges for a current introduced by Kastor and Traschen is found and a number of other new aspects of this current are commented on.

Bethe Algebra using Pure Spinors
Authors: Simon Ekhammar, Dmytro Volin
Preprint number: UUITP19/21
Abstract: We propose a gl(r)covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.

The Eikonal Approach to Gravitational Scattering and Radiation at O(G^3)
Authors: Paolo di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano
Preprint number: UUITP18/21
Abstract: Using N=8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic twoloop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its nonrelativistic (NR) and ultrarelativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential subregion. This task is efficiently carried out by using the method of differential equations with complete nearstatic boundary conditions. In contrast to the potentialregion result, the physical deflection angle includes radiationreaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energymomentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic treelevel amplitude, we are able to treat N=8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein's gravity by the addition of the radiationreaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

Scattering Massive String Resonances through FieldTheory Methods
Authors: Max Guillen, Henrik Johansson, Renann Lipinski Jusinskas, Oliver Schlotterer
Preprint number: UUITP17/21
Abstract: We present a new method, exact in alpha', to explicitly compute string treelevel amplitudes involving one massive state and any number of massless ones. This construction relies on the socalled twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the modulispace integrand of all amplitudes with one massive state using BerendsGiele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional typeI and typeII superstrings.